Aircraft: C172
Phase of flight: Final Approach
Anomaly: Conflict NMAC; Deviation / Discrepancy - Procedural FAR; Deviation / Discrepancy - Procedural Published Material / Policy

My student was preforming pattern work at ZZZ. Traffic pattern altitude being used was 1;800 feet. Conditions were VFR. My student made his crosswind; downwind; and final calls every time. At the same time a C182 was operating for a skydive operation out of ZZZ. My students downwinds were always flown to provide clearance for the skydivers designated landing zone. Throughout his 7 landings in the C172; a PT-17 Stearman joined the pattern; not making any radio communication calls so the student paid extra attention to focus on where the Stearman was operating. The Stearman continued to fly low patterns at about 1;300 feet; with tight downwinds right over the skydiving drop zone. The Stearman sometimes would not even take off from the runway. They would add power then come to a complete stop at the end of the runway and taxi back. While the student was downwind midfield; the skydive C182 was holding short of the runway and made a CTAF call they were waiting for the Stearman to to depart.When the student turned base about 1/2 mile from the runway; the C182 announced they were departing. The student then turned to final and made his radio calls. Flaps were extended about 25 to 30 degrees and the student was coming in at about 70 to 75 MPH. At about 500 feet and 1/4 mile final; the Stearman came down in front of the students C172 about 400 feet away in a rapidly descending base to final and cut right in front of the student. The student had no choice but to abort the landing and go-around since they descended to a lower altitude in front of him. The made a CTAF call on 122.8; '<tail number> going around; aircraft on runway'. Adding full throttle and waiting for a positive rate of climb the student retracted the flaps. The student's initial thought was to just fly runway heading and perform a go around but because of the lack of communication his instincts told him they would perform a touch and go. He then made a 30 degree turn to the right of the runway then turned left to fly parallel to the runway and watched below for the Stearman as he gained altitude. To no surprise the Stearman was performing a touch and go.If my student had flown runway heading the Stearman more than likely would have ascended from under him. If he was any lower on my glide slope; and due to lack of communication from the high performance Stearman; his high wing aircraft would not have seen anyone above him; and the Stearman biplanes nature would not have seen him below them and they would have collided on the displaced threshold. The student had plenty of fuel and flew to the west of ZZZ and waited for them to land before returning. The way the pilots of the Stearman were flying a high performance aircraft with no radio; contrary to the flow of traffic; and without observing Part 91 right of way rules while conducting their operations poses a significant safety hazard. An instructor pilot observing their student in the VFR pattern at a non-towered airport reported another aircraft was not communicating via CTAF and flying against the flow of traffic cut the student off on short final causing a NMAC. The student performed an evasive maneuver and a go-around offset from the runway to avoid the traffic.